Germany has fared better than many of its neighbours in suppressing the virus but concerns are mounting that travellers returning from abroad could bring a surge in new COVID-19 cases.
“I think we really need to focus on these returning holidaymakers,” Söder told broadcaster ZDF.
He said local authorities were working on installing testing centres at Bavarian airports “where anyone can be tested for free any time”.
The scheme is expected to be up and running within days.
Bavaria is home to Munich airport, Germany's second-largest after Frankfurt, as well as several smaller airports.
Frankfurt airport also has a coronavirus testing centre but the service there costs between 59 and 139 euros ($67-159).
The southern state of Bavaria was among Germany's hardest hit regions early on in the pandemic, partly because of residents coming back from ski holidays in coronavirus hotspots in Austria.
A beer festival in the Bavarian town of Mitterteich shortly before the March lockdown began has also been blamed for contributing to the spread.
Since then however Bavarian state premier Söder has won widespread praise for his handling of the crisis, including resisting calls for a premature easing of coronavirus restrictions.
Söder, who is also the leader of Chancellor Angela Merkel's Bavarian CSU sister party, has seen his poll ratings soar as a result.
He is now Germans' preferred candidate to succeed Merkel after she steps down next year — even though he is not officially in the running.
Söder has repeatedly said “my place is in Bavaria” but observers believe he may yet join the race.